Forecasting volatilities in option pricing: An application of Bayesian inference

This study investigates the problem of forecasting volatilities used in option pricing models for live cattle and live hog futures. The forecast problem is cast in the framework of Bayesian inference. Six types of individual forecast models are used--GARCH models, ARIMA models, systems of simultaneous equations, systems of seemingly unrelated regressions, a naive model, and an implied volatility model (i.e., the "inverse" Black option model). Volatility forecasts are made with those individual models under two scenarios involving (1) forecasting over three time-to-maturity periods (six months, four months, and two months) and (2) forecasting one month ahead. Composite forecasts are formed via four methods--Bayesian, adaptive, regression, and averaging. The performances of the forecasts are evaluated using error statistics and timing tests.